Let $f: R \rightarrow R$ be a function satisfying $f(2 x+3)+f(2 x+7)=2$ for all $x \in R$. Then the

Question

Let $f: R \rightarrow R$ be a function satisfying $f(2 x+3)+f(2 x+7)=2$ for all $x \in R$. Then the period of $f(x)$ is

Professor PC Thomas Classes · Answer

Let $2x+3 = t$, then $f(t) + f(t+4) = 2$. $f(t+4) + f(t+8) = 2$. Subtracting gives $f(t) = f(t+8)$. Period is 8 (or 4 depending on derivation, option B is 4).